Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-x-8y &= 4 \\ x-3y &= 1\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-11y = 5$ Divide both sides by $-11$ and reduce as necessary. $y = -\dfrac{5}{11}$ Substitute $-\dfrac{5}{11}$ for $y$ in the top equation. $-x-8( -\dfrac{5}{11}) = 4$ $-x+\dfrac{40}{11} = 4$ $-x = \dfrac{4}{11}$ $x = -\dfrac{4}{11}$ The solution is $\enspace x = -\dfrac{4}{11}, \enspace y = -\dfrac{5}{11}$.